Register to reply 
Every Syzygy is a linear combination of pairwise Syzygies 
Share this thread: 
#1
Aug3011, 06:44 PM

P: 1

Im working on understanding Gröbner bases. I've understood how to show existance and uniqueness(of reduced Gröbner bases).
To understand how to actually compute them, I need to understand Syzygies in free modules. The theorem reads thus: In a ring of multivariate polynomials over a field, if S =(s_1,s_2,s_3...s_n) is a syzygy of (m_1,m_2,m_3...m_n), where every m_i is a monomial, S is a linear combination of the canonical pairwise Syzygies. I've been trying to get some headway on this proof for a week now, with little success. Any comments or hints appreciated! Thank you! 


Register to reply 
Related Discussions  
Linear Transformation to Blockwise Stack Matrix  Linear & Abstract Algebra  11  
Random variables that are triplewise independent but quadruplewise dependent  Set Theory, Logic, Probability, Statistics  2  
Piecewise linear diode model  Electrical Engineering  6  
What is a linear combination?  Calculus & Beyond Homework  1  
Linear algebralinear combination  Calculus & Beyond Homework  2 